I need to find the next two numbers in the following sequence.0,13,13,21,34,55,86,139,216,342,550,898,?,?.

I know that the tens place is following a fibonacci sequence, but I can't figure out the pattern in the ones place. 0,13,13,21,34,55,86,139,216,342,550,898 = 0, 1, 1, 2, 5, 8, 13, 21, 34, 55, 89, 144, 233.

So I know what part of the answer would be for the missing two numbers, but I can't figure out the pattern in the ones place.So the answer should be something like: 144(?) and 233(?). I'm not sure how to find that last number?

Hi Brad15!I'm not entirely sure how this could be solved, but I have noticed that for the first five/six terms, there are some interesting terms. When I saw that the numbers were all single digits that appeared to be random, my first instinct was to try modular arithmetic (a good introduction to modular arithmetic can be found here.) When I added the previous two numbers, as in the Fibonacci sequence, and then put the resulting number in mod 5, I ended up with the next number:0 + 3 mod 5 = 33 + 3 mod 5 = 6 mod 5 = 13 + 6 mod 5 = 9 mod 5 = 4But this is where the pattern breaks down. My gut instinct is that this has something to do with the answer, but I'm not sure if it's related.This is a very interesting problem! I'll keep working on it, and I agree with Willey that a hint on where these numbers are used would help greatly!

Thanks!Vysarge

-Vysarge

~~~~~~~~~~~~~Nature uses only the longest threads to weave her patterns, so that each small piece of her fabric reveals the organization of the entire tapestry.-Richard Feynman

Write a small computer program that randomly generates sequences of instructions (or calls to subroutines within the program). The idea would be for it to generate hundreds of little programs that do the sorts of calculations needed to generate the sequence. The program would know the numbers that are expected, and it checks to see if the random program calculates them correctly. If so, you have a solution to your problem. If not, discard the little program and try the next one. You could limit it to addition, subtraction, multiplication, and division and have it create programs of varying length (you'll need to figure that out).

With a few hours work, if you have some programming experience, you can probably figure it out.